Turbo decoding in a receiving communication system is based on the concept of maximum a posteriori probability of bit decisions made on blocks of channel symbols communicated over a communication channel from a turbo encoding transmitting communication system. Conventional turbo-decoding algorithms are based on the assumption that the input sequence to the turbo decoder has been disturbed by a noise process that has a Gaussian distribution. Conventional turbo-decoding algorithms are optimized for Gaussian channels for reducing the bit-error-rate (BER). Conventional turbo decoders are equipped with a decoder reference for providing a mean and a standard deviation as an estimate of the assumed Gaussian channel statistics. However, when the actual channel statistics of the input sequence to the decoder varies significantly from the Gaussian distribution assumption, the turbo decoder performance will degrade. Hence, the conventional turbo-decoding algorithm incorrectly assumes a Gaussian channel in all cases. A coherently demodulated signal will preserve channel statistics in a turbo decoding system. When the channel is non-Gaussian, the conventional turbo-decoding algorithm suffers degraded performance with a reduced BER. Often, the input sequences to the turbo decoder exhibits non-Gaussian statistics, such that, there will be a mismatch between likelihood values assumed by the decoder and the actual likelihood values presented by non-Gaussian channels. This mismatch produces degradation when using decoding from metrics generated from noncoherently demodulated signals, such as with differentially coherent phase shift keying (DPSK) signals. The performance degradation will also occur from channel disturbances with channel memory, such as from fading, regardless of the demodulation method. Hence, the turbo decoding performance suffers with a reduced BER in the presence of a mismatch between the assumed Gaussian channel without fading and a non-Gaussian channel, such as, a Gaussian channel with fading. For DPSK signaling, the output statistics of a differentially coherent demodulator is non-Gaussian. When a metric sequence from a differentially coherent demodulator is fed directly into a conventional turbo decoder, particularly under a fading environment, the mismatch between decoder algorithm assumptions and actual input statistics can result in significant decoder performance degradation.
Referring to prior art FIG. 2, a prior art non-Gaussian M1 histogram of the random variable rk that may be a detected signal in a fading environment is compared to an M1 decoder reference histogram having a Gaussian distribution. The M1 decoder reference is conditioned on the hypothesis that a decoder input value of a +1 data bit was transmitted. The +1 data bit has a mean input value equal to one. The M1 non-Gaussian probability histogram has a normalized height to the M1 decoder reference Gaussian histogram. The M1 histograms are measured at an average received Eb/N0, such as 10 dB. Channel side information of the M1 decoder reference, typically expressed in the form of average bit signal-to-noise ratio (SNR), is provided to the turbo decoder as a reference for characterizing the noise variance of the assumed Gaussian statistics at the input to the decoder. Under some channel conditions, the BER performance can be improved by applying a fixed bias to the channel side information of the M1 decoder reference obtained from the average SNR. The mismatch between the M1 decoder reference Gaussian histogram and the M1 non-Gaussian histogram reduces turbo decoding performance. As the mismatch grows, the BER increases.
Although optimum decoder performance for a non-Gaussian channel can be achieved by modifying the decoder reference based on the actual input statistics to the turbo decoder for various respective channel statistics, such modifications would only be effective for channel statistics having a Gaussian distribution. To correctly match non-Gaussian channel statistics, the turbo decoder algorithm would need to be modified to match metric processing to the non-Gaussian distribution. Such a redevelopment would only be effective during predetermined fading and predetermined noncoherent demodulation methods, and may not be suitable for a steady state Gaussian channel or other non-Gaussian channels. These and other disadvantages are solved or reduced using the invention.